It creates a 'free' LC with the wire / trace, along with providing the very first bit of the charge to the demanding output. As the cap delivers charge, the big caps from the main supply start to provide current to both recharge the local caps and continue providing power to the output. It lessens ringing and thus removes sources for oscillation, especially noticable with very fast output stages that can draw big currents in an instant; it's what keeps it fast and stable At least, that's my way of thinking.

Maybe the C is free but any L would be more like a cost. Maybe it pays for the C.

This is essentially a power consideration, as you naturally want max rail voltage for high amplitude signals.

What if the power angle differs from the subjective issue, in that the max power will not necessarily deliver the best sound at listening levels? This would considerably reduce the metric from 2000uF/amp......

In this I'm reminded of subjective bass response of amps. If you have an amp with a single output pair, bipolar or mosfet, and relatively high Zout, you can actually improve subjective bass response by interposing a small 0.15R resistor into the speaker output line. This promotes overshoot on the voice coil - that is, loss of VC control - but adds a subjectively stronger bass response. Hardly correct in engineering terms, but quite useful when sculpting bass presentation. Perhaps something similar is operating here?

The other aspect you have touched on is decoupling the amp reservoir cap from the power supply filter cap. I use 0.15R between each cap electrode; 0.3R in all. I have found this very greatly improves sonics presumably by greatly reducing speaker earth return currents from intermodulating with charge currents from the rectifier.

Of course, the rail voltage does sag rather more, yet the sound quality is superior. Should this not be the criteria we should address, and if so, why the hell is this happening?

My experience is empirical. I cannot plausibly explain why. But I suspect the issue is much more complex than baseline power calculations suggest.

That said, I applaud what you are doing. Adding some engineering rigour to this vexing issue has been a long time coming....

This here is also closely connected to the grounding scheme of the amplifier. and where the lowest point of impedance for the speaker return currents is formed. I normally have that right at the Center tap of the Transformer. But I have also had good results with a dual-bridge solution where the star point is formed between the rail-caps.
I used this in a Hiraga inspired amplifier some years ago, where I had a dual-bridge- then one large central reservoir followed by a R-C bank for each channel.

People have reported noticeable changes in sound between different power transformers. The power transformer's inductance and resistance are in the circuit whenever the rectifier diodes are conducting. The capacitors are in a circuit, where there are other elements and multiple time constants.

Hugh, you are always on the right path!, perhaps the overshoot behaviour of the voice coil you referred to is another example where the transient response / damping behaviour of the power supply-amplifier is the factor being sought and the value of the capacitor is just one ingredient.

__________________"The test of the machine is the satisfaction it gives you. There isn't any other test. If the machine produces tranquility it's right. If it disturbs you it's wrong until either the machine or your mind is changed." Robert M Pirsig.

This here is also closely connected to the grounding scheme of the amplifier. and where the lowest point of impedance for the speaker return currents is formed. I normally have that right at the Center tap of the Transformer. But I have also had good results with a dual-bridge solution where the star point is formed between the rail-caps.
I used this in a Hiraga inspired amplifier some years ago, where I had a dual-bridge- then one large central reservoir followed by a R-C bank for each channel.

Hugh do you also insert a resistor in the gnd....??

Wouldn't you want the star point at the output of the power supply, or at least after most of the smoothing caps? It seems like the star ground should be kept out of the loop formed by the transformer secondary, rectifier, smoothing caps, and the other end of the secondary or the center tap. Otherwise the voltages induced across the inductance of the smoothing caps' ground conductors by the charging current pulses would get into ALL of the grounds. If the star point is just past the last smoothing cap, then the caps' grounds and the center tap would just be another arm of the star, and none of the charging currents would ever pass through the star ground point, or anything else connected to it.